Device for teaching division



I I I Aug. 11, 1931.

J. E. MGDADE nEVICE FOR TEACHING DIVISION Filed Jan. 2, 1930 TIMES TIMES +9 v+9 0 3458789 I23456789l I||2`I |4I5I I8 IUIII I3I I5 I7I82- v I 34 5 I9 1232 5 3 /Ww L VIVE Il MM..

Patented Aug. 11, 1931 PATENT OFFICE JAMES E. MCDADE, F CHICAGO, ILLINOIS DEVICE FOR TEACHING DIVISION Application led January 2, 1930. 'Serial No. 417,851.

My invention relates to devices for teach ing division and has for its object the provision of a new and improved means by the use of which a pupil can visualize readily the problem which he is required to do and can understand and appreciate the principles underlying the division process, and

can get an understanding particularly with t respect to remainders and the method of computing them.

My device is preferably to be used for teaching short division, the device to be used by the pupil during the time when he is memorizing. The device is intended to visualize the division operation, to be used for giving the pupil extended practice in doing division with the device before he is required to do such work abstractly without the device. When a pupil is taught, for example, that 8 goes into 39 four times and seven over, it is hard for the pupil to understand what the teacher is talking about. Except as the pupil is enabled to understand the principle involved in the division, it is very difficult for him to memorize or familiarize himself with all of the various combinations involved in ordinary short division.

It is the object of my invention to provide si) a device which shows clearly just what the process of division is for giving the pupil the proper background with respect to long division to be studied later. It is one of the objects of my invention to provide means a5 of this type which can be produced very readily at a minimum of expense, the device being preferably such as to be convenient to use and convenient to store or handle. It is another object of my invention to improve V4o devices of this type in sundry details hereinafter pointed out. The preferred means b which I have accomplished my several objects are illustrated in the drawings and are hereinafter specifically described. That by Letters Patent isset forth in the claims.

In the drawings,-

Fig. 1 is a face vievv of a card provided with a plurality of numbers arranged for illustrating the process of dividing by 9;

which I believe to be new and desire to cover Fig. 2 is .a face view of a separately formed card to be used as a slider or finder in connection with the chart or table of Fig.

1 for solving problems in division;

Fig.l 3 is a face view of the chart of Fig. 55 1 with the finder in position thereon for dividing 50 by 9;

Fig. 4 is a face view of a card similar to that shown in Fig. 1 but arranged for effecting division by 7 and 60 Fig. 5 is a view similar to Fig. 3 but showing a slightly different design and arranged for division by 11.

Referring now particularly to Figs. 1, 2 and 3, 10 indicates a card or sheet bearing 65 on its face a table of numbers from 1 to 90 arranged in rows both horizontally and vertically on the card, all of the numbers of the vertical row at the right of the table 11 as p shown being multiples of 9, and the numbers of each horizontal row in the form of device as shown being arranged in serially increasing order toward the right. Along the right-hand edge of the table,-I have pro-v vided a series of numbers from 1 tol 10 op- 75 posite the Arespective rows, such numbers 1 to 10 constituting a scale for cooperation with an index as hereinafter pointed out for indicating the quotient in any desired divi* sion. The numbers of the several horizontal rows of the table all have equal horizontal spacing in the arrangement shown. The able as a whole is indicated by the numeral 11, and the rovv of figures at the right is indicated by the numeral 12.

For use in connection with the table 11 on the leaf 10, I have provided a'slider or finder 13 in the form of a piece of cardboard or other suitable material of sufficient stiffness for convenient use. The upper edge 9U of the finder 13 is offset at an intermediate point to provide a shoulder 14, such shoulder 14 being of a width corresponding substantially to the vertical spacing of the numbers in the table 11. star 15 is provided on the 95 shoulder portion of the finder in such position as to be capable of being readily centered upon any one ofthe numbers of the table 11, such star 15 constituting an index for enabling the user of the device to place 109 the finder in a predetermined critical position with respect to the selected number of the table 11. Upon the upper edge portion of the finder, extending from the shoulder to the end of the device, I have provided a series of numbers arranged serially beginning with 1, such numbers having .a spacing correspondngtothat of the numbers in the horizontal rows of the table 11 and constituting a scale for cooperation With anindex as hereinafter pointed out for indicating the remainder in any desired division. This row of numbers is indicated as a Whole by reference character 16.

Whenever it is desired to 'divide any one ofthe numbers of the table 11 by 9, the finder 13 .is placed vacross. the table With the star 1.5 superposed uponthe number next larger than the one to be divided. For example, in Fig. 3, the star 15 is located'above the number 5l for `ei'ecting Va division of the number 50 by 9. The arrangement is such that the one .of the numbers of the row 12 which is displayed on the table next above the finder 13indicates the quotient orP the stated division, the upper edge of the finder constituting the index for such indication. The arrangement is such, further, that with the left-hand vertical row of numbers of the table 11 serving as Yan index the scale 16 showsftheiremainder. It isthus seen Vthat 9- goes into '50 live times and five over. The arrangement is such that, Whenever 15h-estar 15 is placedy on topof lany one of thennmbers of the table 11, for edecting a division of the next smaller number, the number oi the Vrow 12 .showing nextabove the linder 13 will indicate the quotient and that the number lof therow 16 opposite the row .at the leftfhand side of the table 11 will indicatethe remainder.

Then the pupilis required to divide 5.0 by 9 and. carries out the process of division as. above described bythe use of the device, he readily arrives at the .solution .as above described,-namely, live times and live over. With this information gathered from the use of the device, the pupil is enabledtosee that there .are five complete rows of numbers of the table above the linder, each of such rows having nine numbers, and that there are ivernumbers of an .additional row visibleabove the nder. Inthis Way, he very readily understands not only that 9 Agoes intor50 live times and tive over but also how .and Why such `is the case. he understands readily the principle in volved, Wherefore he is enabled much more easily to do the necessary memorizing for enabling himeasily to handle problems of this type.

In theconstruction shown in Fig. 4, the arrangementis the same in all respects as that above described in .connection with Figs. 1, 2 .and 3, except that the device is That is i to say,

arranged for division by 7 instead of for division by 9. In Fig. 4 the parts are indicated by the same reference characters as Y i those above designated, except that the card is indicated by the numeral 17. The finder 13 shown in Fig. 4L is precisely the same as that shown in Figs. 2 and 3, or may be the same finder.

In the construction shown in Fig. 5, a card 18 is shown arranged for division by 11, such card being provided with numbers from 1 to 77 arranged in seven rows of eleven numbers each. In the construction shown lin Fig. 5, the numbers of each row increase serially toward the left instead of toward the right as in Figs. 1 and t. In View of this change of arrangement with respect to the numbers in the table,the slider device ,19 has its remainder-indicating numbers also arranged in reverse order as compared with the finder 13, the remainder-indicating numbers being indicated as a Wholel by the nu- 1neral20. In the construction shown in.F ig. 5, the quotient indicating numbers .at the right are opposite the lowervportion ofthe top edge line, Whereforethe series of lquotient -indicating numbers begins with ,Zero opposite the iirst horizontal row oitl numbers on the table rather than with `1 as in Figs. 1 and 4. Such rou7 of quotient-indicating numbers is-indicated by the numeral 21.

In the use of the construction as `.s-liovvn in Fig. 5, the .star 15 is pla-ced over. the number next larger than the number to be divided, whereupon the quotient isindicated bythe one et the numbers of the row 21 next Vabove the upper edge ot the finder 19, and theref main ler is indi-cated by the number in Ethe row 2O directly underneath the quotient indicating row. In the example illustrated,.11 is. shown to go into 5S tive times With three over. It Willthus be seen that thedevice of Fig. 5 is perhaps more convenient -or use'as a dividing device than is the construct-ien as shown in Fig. 1. The device of Fig. 5 is not, however, so clear asa device for teaching the principles of divisionand remainders .as is the device of Fig. 1.

While I prefer to employ the construction as shown in Figs. 1 and 4, Withother tables forv division bycorrespondingly small numbers indicated on other cards, or with any desired number ofsuch tables all shown. en a single sheet, vit ris to be understood that my invention is not to be limited yto the form shown in Fig. 1 except so far as the claims may be so limited by the prior art, it being understoodtliat changes may Well be made in the form and arrangement as illustrated in Fig. 5 or otherwise Without departing from the spirit of my invention.

I claim 1. In .a device for solving a problem in division, the combination, of a leatmember having on one face a table comprising Aa plu'- rality of numbers arranged serially in rows inv equally spaced position in one direction and arranged in rows in the cross direction, with the largest numbers in said first named rows respectively successive multiples of a predetermined divisor, a finder having index means adapted readily to be placed over any selected number of said table for indicating the quotient of the number next smaller than the selected number divided by said predetermined divisor, and a number displayed at a predetermined point with respect to the finder indicating said quotient. 2. In a device for solving a problem in division, the combination of a leaf member having on one face a table comprising a plurality of numbers arranged serially in rows in equally spaced position in one direction and arranged in rows in the cross direction, with the largest numbers in said lirst named rows respectively successive multiples of a predetermined divisor, a finder member having index means adapted readily to be placed over any selected number of said table for indicating the quotient of the number next smaller than the selected number divided by said predetermined divisor, index and scale means on said members respectively for indicating said quotient, and

index and scale means on said members respectively for indicating the remainder.

3. In a device for solving a problem in division, the combination of a leaf member having on one face a table comprising a plurality of numbers arranged serially in rows in one direction and arranged also in rows in the cross direction, with the largest numbers in said first named rows respectively successive multiples of a predetermined divisor, a linder member in the form of a card having a shoulder in its top edge for indicating the critical position of said member with respect to a selected number 0f said table for determining the quotient of said number divided by said predetermined divisor, and scale means on one of said members adapted by reference to index means of the other member to indicate said quotient.

4. In a device for solving a problem in division, the combination of a leaf member having a table thereon comprising a plu` rality of numbers arranged in rows both horizontally and vertically, with one of said .i rows in one direction made up of multiples of a predetermined divisor and with all of tue numbers in each of the rows in the cross direction differing from such multiple in said row by less than the value of said divisor, and a finder member comprising index means for enabling the user to place the finder in predetermined critical position on said table with respect to a selected dividend on said table for indicating the quotient of said selected dividend divided by said predetermined divisor, said members compris ing scale means on one member adapted by reference to index means on the other member to indicate said quotient.

5. In a device for solving a problem in division, the combination of a leaf member having a table thereon comprising a plurality of numbers arranged in rows both horizontally and vertically, with one of said rows in one direction made up of multiples of a predetermined divisor and with all of the numbers in each of the rows in the cross direction diering from such multiple in said row by less than the value of said divisor, and a finder member comprising in` dex means for enabling the user to place the finder in predetermined critical position on said table with respect to a selected dividend on said table for indicating the quotient of said selected dividend divided by said predetermined divisor, said members comprising scale means on one member adapted by reference to index means of the other member to indicate said quotient and scale means on one member adapted by reference to index means of the other member to indicate the remainder.

JAMES E. MCDADE. 

